To unravel this issue, we performed specific heat (\(C_p\) ) measurement as a function of temperature, Fig. REF (a). Interestingly, there is no clear transition in the unaided eye \(C_p\)  curve depicted in the main panel of the figure. However, a magnified view of the \(C_p/T\)  curve, shown at the inset, indicates a very subtle and broad hump only around \(T_C\) , suggestive of a disordered system for which competing magnetic interactions and frustration lead to short-range correlations, in a way that the magnonic contribution is masked by the phononic one which becomes relevant at higher temperatures. Similar behavior is commonly observed in disordered DPs [1]}, [2]}, [3]}. The absence of anomaly at \(T^{*}\)  indicates that this is not related to any conventional magnetic or structural transition. This is in agreement with previous studies of Ir-based DPs as La\(_{2-x}\) Sr\(_x\) CoIrO\(_6\)  [4]}, [5]} and La\(_2\) ZnIrO\(_6\)  [6]}, for which NPD indicate only one magnetic ordering resulting in NCM with two interpenetrating AFM superstructures for Co/Fe and Ir sites, the weak magnetization observed in these compounds coming from spin canting.
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